Well proximiity ammo was great, but i though it was a discussion about the firecontrol of the 'big guns'. The 40mm bofors used the very same fine instrument to aim at the incoming craft as centuries before : the human eye. There was no radar control for the medium aa guns, though I am not sure about the 5" ones. Probably they had, I know KM ships better, Tirpitz used the LW`s Wurzburg set for heavy AAA fire control.
Back on radar, range estimation doesn`t seem to be a huge problem. This could be done fairly well with early war, longwave radar sets to about 20k (range largely depends on target size). The problem was getting the bearing data, which they had troubles with due to the poor resulution. But even mid-war German sets, which operated at far longer waves (less precision, but also less noise from sea waves) were capable of 0.5 degree bearing accuaracy, which gives around 50 or 100?meter dispersion at the top edge of practical ww2 naval engagments. Already good enough to hit a 250m long ship, especially with gun dispersion in account...
later war Allied radar with it`s small centimetric wavelenght must have been more precise, but if both sides possess the neccesary precision to hit the enemy, there`s not much difference in actual hit probabilities, assuming Japanese sets were good as the KMs.
